Finite Group Databasebeta

← #11911069

Subgroups — #11911069

Order 1152.

2545 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C3×#5515C212yesmaximal, complemented
3#10595080C212yesmaximal, complemented
4#10595079C211yesmaximal, characteristic, complemented
5#10595075C212yesmaximal, complemented
6#10595074C212yesmaximal, complemented
7#10595035C212yesmaximal, complemented
8#10595018C212yesmaximal, complemented
9#10594920C211yesmaximal, characteristic, complemented
10#10594663C212yesmaximal, complemented
11#10594658C211yesmaximal, characteristic, complemented
12#10594652C212yesmaximal, complemented
13#10594620C212yesmaximal, complemented
14#10594610C211yesmaximal, characteristic, complemented
15#10594593C212yesmaximal, complemented
16#10594519C211yesmaximal, characteristic, complemented
17#10594483C211yesmaximal, characteristic, complemented
18#10594468C212yesmaximal, complemented
19#10594467C212yesmaximal, complemented
20#86458—32nomaximal
21C22×C4⋊(C3⋊D3)C2212yescomplemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×#3811C2211yescharacteristic
25C2×#3811C2212yescomplemented
26C2×#3805C2211yescharacteristic, complemented
27C2×D3×D12C2212yescomplemented
28C2×#3799C2212yescomplemented
29C2×C32×C4⋊C4C2211yescharacteristic, complemented
30C2×#3752C2212yescomplemented
31#64104C2211yescharacteristic
32#64104C2212yescomplemented
33#64104C2212yescomplemented
34#64104C2211yescharacteristic, complemented
35#64104C2211yescharacteristic, complemented
36#64104C2211yescharacteristic, complemented
37C3×#930C2212yes—
38C3×#929C2212yescomplemented
39C3×#929C2212yescomplemented
40C3×C4×#67C2212yescomplemented
41C3×C4×#67C2212yescomplemented
42C3×#924C2212yescomplemented
43C3×#898C2212yescomplemented
44C3×#898C2212yescomplemented
45C3×#896C2212yescomplemented
46C3×#896C2212yescomplemented
47C3×#894C2212yescomplemented
48C3×#894C2212yescomplemented
49C3×#889C2212yescomplemented
50C3×#889C2212yescomplemented
51#63981C2212yes—
52#63981C2212yescomplemented
53#63981C2212yescomplemented
54#63974C2211yescharacteristic, complemented
55#63974C2212yescomplemented
56#63962C2212yescomplemented
57#63957C2211yescharacteristic, complemented
58#63923C2212yescomplemented
59#63923C2212yescomplemented
60#63923C2212yescomplemented
61#63923C2212yescomplemented
62#63922C2212yescomplemented
63#63921C2211yescharacteristic, complemented
64#63921C2211yescharacteristic, complemented
65D3×(C2×D3)⋊C4C2212yescomplemented
66#63912C2211yescharacteristic, complemented
67#63912C2211yescharacteristic, complemented
68#63911C2212yescomplemented
69#63910C2212yescomplemented
70#63910C2212yescomplemented
71#63910C2212yescomplemented
72#63910C2212yescomplemented
73#63910C2212yescomplemented
74#63910C2212yescomplemented
75#63910C2212yescomplemented
76#63910C2212yescomplemented
77#63909C2212yescomplemented
78#63909C2212yescomplemented
79#63907C2212yescomplemented
80#63906C2212yescomplemented
81#63904C2212yescomplemented
82#63897C2212yescomplemented
83#63897C2212yescomplemented
84#63897C2212yescomplemented
85#63897C2212yescomplemented
86#63895C2212yescomplemented
87#63894C2212yescomplemented
88#63894C2212yescomplemented
89#63890C2212yescomplemented
90#63888C2212yescomplemented
91#63886C2212yescomplemented
92#63883C2211yescharacteristic, complemented
93#63883C2211yescharacteristic, complemented
94#63881C2212yescomplemented
95#63881C2212yescomplemented
96#63880C2212yescomplemented
97#63868C2212yescomplemented
98#63865C2211yescharacteristic, complemented
99#63865C2211yescharacteristic, complemented
100#63864C2212yescomplemented
101#63854C2212yescomplemented
102#63853C2212yescomplemented
103#63853C2212yescomplemented
104#63852C2212yescomplemented
105#63850C2212yescomplemented
106#63848C2212yescomplemented
107#63836C2212yescomplemented
108C3×#539—32no—
109#5711—32no—
110#5709—32no—
111#5704—32no—
112#5704—32no—
113#5700—32no—
114#5697—32no—
115#5695—32no—
116#5692—32no—
117#5666—32no—
118#5663—32no—
119#5656—32no—
120#5654—32no—
121#5653—32no—
122#5653—32no—
123#5653—32no—
124D3×#123—32no—
125#5647—32no—
126#5644—32no—
127#5637—32no—
128#5630—32no—
129#5630—32no—
130#5629—32no—
131#5610—32no—
132#5609—32no—
133#5556—32no—
134#5554—32no—
135#5550—32no—
136D4×D12—32no—
137#5515D312yescomplemented
138C2×#895—32no—
139C2×#895—61no—
140C23×C3⋊D3C2311yescharacteristic
141C23×C3⋊D3C2312yes—
142C22×D32C2311yescharacteristic
143C22×D32C2312yes—
144C22×C32×C4C2311yescharacteristic
145C22×C32×C4C2312yes—
146C22×C3⋊Dic3C2311yescharacteristic
147C2×C4⋊(C3⋊D3)—44no—
148C2×C4⋊(C3⋊D3)—42no—
149C2×C4⋊(C3⋊D3)C2312yes—
150C2×C4⋊(C3⋊D3)C2312yes—
151C2×C4⋊(C3⋊D3)C2311yescharacteristic
152C2×C4⋊(C3⋊D3)C2312yes—
153C2×C4⋊(C3⋊D3)C2312yes—
154C2×C4⋊(C3⋊D3)C2312yes—
155C2×C4⋊(C3⋊D3)C2311yescharacteristic
156C2×C4×C3⋊D3—42no—
157C2×C4×C3⋊D3C2311yescharacteristic
158C2×C4×C3⋊D3C2311yescharacteristic
159C2×C4×C3⋊D3C2311yescharacteristic
160C2×C4×C3⋊D3C2311yescharacteristic
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×D12C2312yes—
164C2×C3×C4×D3C2312yes—
165C2×C3×C4×D3C2312yes—
166C2×C3×Dic6C2312yes—
167#3811—42no—
168#3811—44no—
169C2×#627C2311yescharacteristic
170C2×#626C2312yes—
171C2×#626C2312yes—
172C2×#626C2312yes—
173C2×#626C2312yes—
174C2×#626C2312yes—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#625C2311yescharacteristic
180C2×#624C2311yescharacteristic
181C2×#624C2312yes—
182C2×#624C2311yescharacteristic
183C2×#624C2312yes—
184C2×#624C2312yes—
185C2×#624C2311yescharacteristic
186#3805—42no—
187C2×D3×Dic3C2312yes—
188D3×D12—44no—
189#3799—44no—
190C32×C4⋊C4C2311yescharacteristic
191C32×C4⋊C4C2312yes—
192C32×C4⋊C4C2311yescharacteristic
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3752C2312yes—
197C3×#217C2312yes—
198C3×#217C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×(C2×D3)⋊C4C2312yes—
201C3×(C2×D3)⋊C4C2312yes—
202C3×(C2×D3)⋊C4C2312yes—
203C3×(C2×D3)⋊C4C2312yes—
204C3×(C2×D3)⋊C4C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×C4⋊Dic3C2312yes—
208C3×C4⋊Dic3C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×Dic3⋊C4C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×Dic3⋊C4C2312yes—
217C3×C4×Dic3C2312yes—
218C3×C4×Dic3C2312yes—
219#3724C2311yescharacteristic
220#3724C2311yescharacteristic
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226#3722C2312yes—
227#3722C2312yes—
228#3722C2312yes—
229#3722C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234Dic32C2312yes—
235#3534—91noSylow
236C2×#239—32no—
237C2×#237—32no—
238C2×D3×D4—32no—
239C2×D3×D4—32no—
240C2×D3×D4—32no—
241C2×D3×D4—32no—
242C2×#235—32no—
243C22×D12—32no—
244C22×D12—32no—
245C22×D12—32no—
246C22×D12—32no—
247C22×D12—61no—
248C22×D12—62no—
249C22×C4×D3—32no—
250C22×C4×D3—61no—
251C3×#126—32no—
252C3×#126—32no—
253C3×#125—32no—
254C3×#125—32no—
255C3×#123—32no—
256C3×#123—32no—
257C3×#123—32no—
258C3×#123—32no—
259C3×C22⋊Q8—32no—
260C3×C22⋊Q8—32no—
261C3×C22⋊Q8—32no—
262C3×#121—32no—
263C3×C4×D4—32no—
264C3×C4×D4—32no—
265C2×C3×C4⋊C4—21no—
266C2×C3×C4⋊C4C2×D312yescomplemented
267#947—32no—
268#947—32no—
269#946—32no—
270#940—32no—
271#939—32no—
272#937—32no—
273#937—32no—
274#937—32no—
275#937—32no—
276#935—32no—
277#930—32no—
278#930—32no—
279#930—32no—
280#930C2×D312yes—
281#929—32no—
282#929C2×D312yescomplemented
283#929C2×D312yescomplemented
284C4×#67—32no—
285C4×#67C2×D312yescomplemented
286C4×#67C2×D312yescomplemented
287C2×(C2×D3)⋊C4—32no—
288C2×(C2×D3)⋊C4—32no—
289C2×(C2×D3)⋊C4—32no—
290C2×(C2×D3)⋊C4—62no—
291#924C2×D312yescomplemented
292#898—32no—
293#898—32no—
294#898—32no—
295#898C2×D312yescomplemented
296#898C2×D312yescomplemented
297#897—32no—
298#896—32no—
299#896—32no—
300#896—32no—
301#896—32no—
302#896C2×D312yescomplemented
303#896C2×D312yescomplemented
304#895—32no—
305#895—32no—
306#895—32no—
307#895—32no—
308#895—32no—
309#895—32no—
310#895—32no—
311#895—32no—
312#895—32no—
313#895—32no—
314#895—32no—
315#895—32no—
316#895—32no—
317#895—32no—
318#895—32no—
319#895—32no—
320#895—32no—
321#895—32no—
322#895—32no—
323#895—61no—
324#895—61no—
325#895—61no—
326#895—61no—
327#895—62no—
328#895—62no—
329#894—32no—
330#894—32no—
331#894—32no—
332#894—32no—
333#894—32no—
334#894—32no—
335#894—32no—
336#894—32no—
337#894—32no—
338#894—32no—
339#894—32no—
340#894—32no—
341#894—32no—
342#894C2×D312yescomplemented
343#894C2×D312yescomplemented
344#893—32no—
345#893—32no—
346#893—32no—
347#893—32no—
348#893—32no—
349#892—32no—
350D3×C4⋊C4—32no—
351D3×C4⋊C4—32no—
352#889C2×D312yescomplemented
353#889C2×D312yescomplemented
354#886—32no—
355#886—32no—
356#885—32no—
357#885—32no—
358#884—32no—
359#884—32no—
360#884—32no—
361#884—32no—
362#884—32no—
363#884—32no—
364#884—32no—
365#884—32no—
366#884—32no—
367#884—32no—
368#884—32no—
369#883—32no—
370#883—32no—
371#883—32no—
372#882—32no—
373#882—32no—
374#882—32no—
375#882—32no—
376#882—32no—
377#882—32no—
378#882—32no—
379#882—32no—
380#882—32no—
381#882—32no—
382#882—32no—
383#882—32no—
384#67⋊C4—32no—
385#67⋊C4—32no—
386#67⋊C4—32no—
387D3×C22⋊C4—32no—
388D3×C22⋊C4—32no—
389D3×C22⋊C4—32no—
390D3×C22⋊C4—32no—
391D3×C22⋊C4—32no—
392D3×C22⋊C4—32no—
393#877—32no—
394#876—32no—
395#875—32no—
396#875—32no—
397#874—32no—
398C4×D12—32no—
399C4×D12—32no—
400C4×D12—32no—
401#872—32no—
402C23×C32C2411yescharacteristic
403C22×C3⋊D3—22no—
404C22×C3⋊D3—22no—
405C22×C3⋊D3—24no—
406C22×C3⋊D3—41no—
407C22×C3⋊D3—42no—
408C22×C3⋊D3—42no—
409C22×C3⋊D3C2412yes—
410C22×C3⋊D3C2411yescharacteristic
411C22×C3⋊D3C2412yes—
412C22×C3⋊D3C2411yescharacteristic
413C22×C3×D3C2412yes—
414C22×C3×D3C2412yes—
415C2×D32—22no—
416C2×D32—41no—
417C2×D32—42no—
418C2×D32—42no—
419C2×D32—41no—
420C2×D32—42no—
421C2×C32×C4—22no—
422C2×C32×C4—42no—
423C2×C32×C4C2412yes—
424C2×C32×C4C2412yes—
425C2×C32×C4C2411yescharacteristic
426C2×C32×C4C2411yescharacteristic
427C2×C3⋊Dic3—22no—
428C2×C3⋊Dic3C2411yescharacteristic
429C2×C3⋊Dic3C2411yescharacteristic
430C4⋊(C3⋊D3)—24no—
431C4⋊(C3⋊D3)—24no—
432C4⋊(C3⋊D3)—41no—
433C4⋊(C3⋊D3)—42no—
434C4⋊(C3⋊D3)—41no—
435C4⋊(C3⋊D3)—42no—
436C4⋊(C3⋊D3)—42no—
437C4×C3⋊D3—41no—
438C4×C3⋊D3—41no—
439C4×C3⋊D3—41no—
440C4×C3⋊D3—41no—
441C3×#67—24no—
442C3×#67—24no—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2412yes—
445C2×C3×Dic3C2412yes—
446C2×C3×Dic3C2412yes—
447C2×C3×Dic3C2412yes—
448C2×C3×Dic3C2412yes—
449C3×D12—42no—
450C3×C4×D3—42no—
451C3×C4×D3—42no—
452C3×Dic6—42no—
453#627—41no—
454#626—24no—
455#626—42no—
456#626—42no—
457#626—42no—
458#626—42no—
459#626—42no—
460#626—42no—
461#626—42no—
462#626—42no—
463#625—41no—
464#624—22no—
465#624—42no—
466#624—41no—
467#624—42no—
468#624—42no—
469#624—41no—
470D3×Dic3—42no—
471#562—92no—
472#560—92no—
473#553—92no—
474#551—92no—
475#546—92no—
476#546—92no—
477#546—92no—
478D42—92no—
479#540—92no—
480#539—32no—
481#539—91no—
482#538—92no—
483#538—91no—
484#537—91no—
485#534—91no—
486#534—92no—
487#525—91no—
488C2×#123—91no—
489C2×#121—91no—
490C23×D3—32no—
491C23×D3—32no—
492C23×D3—32no—
493C23×D3—32no—
494C23×D3—32no—
495C23×D3—32no—
496C23×D3—61no—
497C23×D3—62no—
498C2×C3×Q8—32no—
499C2×C3×D4—32no—
500C2×C3×D4—32no—
501C2×C3×D4—32no—
502C22×C3×C4—21no—
503C22×C3×C4—22no—
504C22×C3×C4—32no—
505C22×C3×C4—32no—
506C22×C3×C4C22×D312yes—
507C22×C3×C4C22×D312yes—
508C22×C3×C4C22×D312yes—
509C2×#67—32no—
510C2×#67—32no—
511C2×#67—32no—
512C2×#67—32no—
513C2×#67—32no—
514C2×#67—32no—
515C2×#67—32no—
516C2×#67—32no—
517C2×#67—32no—
518C2×#67—32no—
519C2×#67C22×D312yes—
520C2×#67C22×D312yes—
521C22×Dic3—32no—
522C22×Dic3—32no—
523C22×Dic3—61no—
524#239—124no—
525#237—124no—
526D3×D4—124no—
527D3×D4—124no—
528D3×D4—124no—
529D3×D4—124no—
530#235—124no—
531C2×D12—32no—
532C2×D12—32no—
533C2×D12—32no—
534C2×D12—32no—
535C2×D12—32no—
536C2×D12—32no—
537C2×D12—32no—
538C2×D12—32no—
539C2×D12—32no—
540C2×D12—32no—
541C2×D12—32no—
542C2×D12—32no—
543C2×D12—32no—
544C2×D12—32no—
545C2×D12—32no—
546C2×D12—32no—
547C2×D12—32no—
548C2×D12—32no—
549C2×D12—32no—
550C2×D12—32no—
551C2×D12—32no—
552C2×D12—62no—
553C2×D12—62no—
554C2×D12—61no—
555C2×D12—62no—
556C2×D12—62no—
557C2×D12—61no—
558C2×D12—62no—
559C2×D12—124no—
560C2×D12—124no—
561C2×D12—124no—
562C2×D12—124no—
563C2×D12—124no—
564C2×D12—128no—
565C2×D12C22×D312yes—
566C2×C4×D3—32no—
567C2×C4×D3—32no—
568C2×C4×D3—32no—
569C2×C4×D3—32no—
570C2×C4×D3—32no—
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—61no—
581C2×C4×D3—61no—
582C2×C4×D3—61no—
583C2×C4×D3—61no—
584C2×C4×D3—124no—
585C2×C4×D3—124no—
586C2×C4×D3C22×D312yes—
587C2×C4×D3C22×D312yes—
588C2×Dic6—32no—
589C2×Dic6C22×D312yes—
590C3×C4⋊C4—21no—
591C3×C4⋊C4—22no—
592C3×C4⋊C4—21no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C4⋊C4—32no—
597C3×C4⋊C4—32no—
598C3×C4⋊C4—32no—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4—32no—
603C3×C4⋊C4C22×D312yes—
604C3×C4⋊C4C22×D312yes—
605C3×C4⋊C4C22×D312yes—
606C3×C4⋊C4C22×D312yes—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—32no—
610C3×C22⋊C4—32no—
611C3×C22⋊C4—32no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4—32no—
615C3×C22⋊C4—32no—
616C3×C22⋊C4—32no—
617C3×C42—32no—
618C3×C42—32no—
619#217—32no—
620#217—32no—
621#217C22×D312yes—
622#217C22×D312yes—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—32no—
626(C2×D3)⋊C4—32no—
627(C2×D3)⋊C4—32no—
628(C2×D3)⋊C4—32no—
629(C2×D3)⋊C4—32no—
630(C2×D3)⋊C4—32no—
631(C2×D3)⋊C4—32no—
632(C2×D3)⋊C4—32no—
633(C2×D3)⋊C4—32no—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—32no—
640(C2×D3)⋊C4—32no—
641(C2×D3)⋊C4—32no—
642(C2×D3)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—32no—
648(C2×D3)⋊C4—32no—
649(C2×D3)⋊C4—32no—
650(C2×D3)⋊C4—32no—
651(C2×D3)⋊C4—62no—
652(C2×D3)⋊C4—62no—
653(C2×D3)⋊C4—62no—
654(C2×D3)⋊C4—62no—
655(C2×D3)⋊C4C22×D312yes—
656(C2×D3)⋊C4C22×D312yes—
657(C2×D3)⋊C4C22×D312yes—
658(C2×D3)⋊C4C22×D312yes—
659(C2×D3)⋊C4C22×D312yes—
660(C2×D3)⋊C4C22×D312yes—
661(C2×D3)⋊C4C22×D312yes—
662(C2×D3)⋊C4C22×D312yes—
663C4⋊Dic3—32no—
664C4⋊Dic3—32no—
665C4⋊Dic3C22×D312yes—
666C4⋊Dic3C22×D312yes—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4C22×D312yes—
672Dic3⋊C4C22×D312yes—
673Dic3⋊C4C22×D312yes—
674Dic3⋊C4C22×D312yes—
675Dic3⋊C4C22×D312yes—
676Dic3⋊C4C22×D312yes—
677Dic3⋊C4C22×D312yes—
678Dic3⋊C4C22×D312yes—
679C4×Dic3—32no—
680C4×Dic3—32no—
681C4×Dic3C22×D312yes—
682C4×Dic3C22×D312yes—
683C22×C32—21no—
684C22×C32—21no—
685C22×C32H(5,𝔽2)12yes—
686C22×C32C2511yescharacteristic
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—22no—
691C2×C3⋊D3—22no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—22no—
694C2×C3⋊D3—22no—
695C2×C3⋊D3—22no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3—22no—
698C2×C3⋊D3—44no—
699C2×C3⋊D3—84no—
700C2×C3⋊D3H(5,𝔽2)12yes—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—22no—
704C2×C3×D3—22no—
705C2×C3×D3—22no—
706C2×C3×D3—22no—
707D32—82no—
708D32—84no—
709C32×C4—21no—
710C32×C4—21no—
711C32×C4—22no—
712C32×C4—22no—
713C3⋊Dic3—21no—
714C3⋊Dic3—21no—
715C3×Dic3—22no—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—22no—
720C3×Dic3—22no—
721C2×#41—92no—
722C2×#41—91no—
723C22×D4—92no—
724C22×D4—91no—
725C22×D4—92no—
726C22×D4—91no—
727C22×D4—92no—
728C23×C4—91no—
729#127—92no—
730#126—32no—
731#126—32no—
732#126—92no—
733#126—92no—
734#125—32no—
735#125—32no—
736#124—92no—
737#124—92no—
738#124—92no—
739#123—32no—
740#123—32no—
741#123—32no—
742#123—32no—
743#123—92no—
744#123—92no—
745#123—92no—
746#123—92no—
747#123—92no—
748#123—92no—
749#123—92no—
750#123—92no—
751#123—92no—
752#123—92no—
753C22⋊Q8—32no—
754C22⋊Q8—32no—
755C22⋊Q8—32no—
756C22⋊Q8—91no—
757C22⋊Q8—91no—
758C22⋊Q8—92no—
759C22⋊Q8—92no—
760#121—32no—
761#121—91no—
762#121—91no—
763#121—92no—
764#121—92no—
765#121—92no—
766#121—92no—
767#121—92no—
768#121—92no—
769#121—92no—
770#121—92no—
771#121—92no—
772#121—92no—
773#121—92no—
774#121—92no—
775#121—91no—
776#121—91no—
777#121—91no—
778#121—91no—
779#121—92no—
780#121—92no—
781#120—92no—
782#120—92no—
783#120—92no—
784#120—92no—
785#120—92no—
786#120—92no—
787#120—92no—
788#120—92no—
789C4×D4—32no—
790C4×D4—32no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796C4×D4—92no—
797#117—92no—
798#117—91no—
799C2×C4⋊C4—91no—
800C2×C4⋊C4—91no—
801C2×C4⋊C4D3211yescharacteristic, complemented
802C2×C22⋊C4—91no—
803C2×C22⋊C4—91no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—92no—
806C2×C22⋊C4—92no—
807C2×C22⋊C4—92no—
808C23×C3—21no—
809C23×C3—32no—
810C23×C3—32no—
811C23×C3C23×D312yes—
812C22×D3—32no—
813C22×D3—32no—
814C22×D3—32no—
815C22×D3—32no—
816C22×D3—32no—
817C22×D3—32no—
818C22×D3—61no—
819C22×D3—61no—
820C22×D3—62no—
821C22×D3—62no—
822C22×D3—64no—
823C22×D3—64no—
824C22×D3—64no—
825C22×D3—64no—
826C22×D3—64no—
827C22×D3—64no—
828C22×D3—122no—
829C22×D3—124no—
830C22×D3—122no—
831C22×D3—122no—
832C22×D3—122no—
833C22×D3—122no—
834C22×D3—122no—
835C22×D3—122no—
836C22×D3—122no—
837C22×D3—122no—
838C22×D3—122no—
839C22×D3—122no—
840C22×D3—122no—
841C22×D3—122no—
842C22×D3—122no—
843C22×D3—122no—
844C22×D3—124no—
845C22×D3—124no—
846C22×D3C23×D312yes—
847C22×D3C23×D312yes—
848C3×Q8—122no—
849C3×D4—64no—
850C3×D4—64no—
851C3×D4—122no—
852C2×C3×C4—24no—
853C2×C3×C4—24no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—22no—
857C2×C3×C4—22no—
858C2×C3×C4—32no—
859C2×C3×C4—32no—
860C2×C3×C4—32no—
861C2×C3×C4—32no—
862C2×C3×C4—32no—
863C2×C3×C4—32no—
864C2×C3×C4—42no—
865C2×C3×C4—42no—
866C2×C3×C4—44no—
867C2×C3×C4—122no—
868C2×C3×C4—122no—
869C2×C3×C4C23×D312yes—
870C2×C3×C4C23×D312yes—
871C2×C3×C4C23×D312yes—
872C2×C3×C4C23×D312yes—
873C2×C3×C4C23×D312yes—
874C2×C3×C4C23×D312yes—
875#67—24no—
876#67—24no—
877#67—64no—
878#67—122no—
879#67—122no—
880#67—122no—
881#67—122no—
882#67—122no—
883#67—122no—
884#67—122no—
885#67—122no—
886#67—122no—
887C2×Dic3—32no—
888C2×Dic3—32no—
889C2×Dic3—61no—
890C2×Dic3—61no—
891C2×Dic3—64no—
892C2×Dic3—122no—
893C2×Dic3—122no—
894C2×Dic3C23×D312yes—
895C2×Dic3C23×D312yes—
896C2×Dic3C23×D312yes—
897C2×Dic3C23×D312yes—
898C2×Dic3C23×D312yes—
899C2×Dic3C23×D312yes—
900D12—42no—
901D12—64no—
902D12—64no—
903D12—64no—
904D12—64no—
905D12—64no—
906D12—124no—
907D12—124no—
908D12—122no—
909D12—122no—
910D12—122no—
911D12—122no—
912D12—122no—
913D12—122no—
914D12—122no—
915D12—122no—
916D12—122no—
917D12—124no—
918D12—122no—
919D12—124no—
920D12—124no—
921D12—122no—
922D12—122no—
923D12—122no—
924D12—122no—
925D12—122no—
926D12—122no—
927D12—122no—
928D12—122no—
929C4×D3—42no—
930C4×D3—42no—
931C4×D3—64no—
932C4×D3—122no—
933C4×D3—122no—
934C4×D3—122no—
935C4×D3—122no—
936C4×D3—122no—
937C4×D3—122no—
938C4×D3—122no—
939C4×D3—122no—
940C4×D3—122no—
941C4×D3—122no—
942C4×D3—122no—
943C4×D3—122no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948C4×D3—122no—
949Dic6—42no—
950Dic6—122no—
951C2×C32—22no—
952C2×C32C2×H(5,𝔽2)11yescharacteristic
953C2×C32C2×H(5,𝔽2)11yescharacteristic
954C2×C32#58511yescharacteristic
955C3⋊D3—22no—
956C3⋊D3—41no—
957C3⋊D3—42no—
958C3⋊D3—42no—
959C3×D3—42no—
960C3×D3—42no—
961C24—91no—
962C24—92no—
963C24—91no—
964C24—92no—
965#41—364no—
966#41—362no—
967C2×Q8—32no—
968C2×Q8—91no—
969C2×D4—32no—
970C2×D4—32no—
971C2×D4—32no—
972C2×D4—92no—
973C2×D4—92no—
974C2×D4—92no—
975C2×D4—92no—
976C2×D4—92no—
977C2×D4—92no—
978C2×D4—92no—
979C2×D4—92no—
980C2×D4—92no—
981C2×D4—91no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—91no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4—91no—
988C2×D4—92no—
989C2×D4—362no—
990C2×D4—364no—
991C2×D4—364no—
992C2×D4—362no—
993C2×D4—364no—
994C22×C4—32no—
995C22×C4—32no—
996C22×C4—91no—
997C22×C4—91no—
998C22×C4—92no—
999C22×C4—92no—
1000C22×C4—91no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—91no—
1004C22×C4—91no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—91no—
1008C22×C4—362no—
1009C22×C4C2×D3211yescharacteristic
1010C22×C4C2×D3212yes—
1011C4⋊C4—32no—
1012C4⋊C4—32no—
1013C4⋊C4—32no—
1014C4⋊C4—32no—
1015C4⋊C4—32no—
1016C4⋊C4—32no—
1017C4⋊C4—32no—
1018C4⋊C4—32no—
1019C4⋊C4—32no—
1020C4⋊C4—32no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4—91no—
1024C4⋊C4—91no—
1025C4⋊C4C2×D3211yescharacteristic
1026C4⋊C4C2×D3212yes—
1027C4⋊C4C2×D3211yescharacteristic
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—32no—
1036C22⋊C4—32no—
1037C22⋊C4—32no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4—92no—
1053C42—32no—
1054C42—32no—
1055C42—92no—
1056C22×C3—22no—
1057C22×C3—22no—
1058C22×C3—22no—
1059C22×C3—22no—
1060C22×C3—22no—
1061C22×C3—21no—
1062C22×C3—62no—
1063C22×C3—62no—
1064C22×C3—62no—
1065C22×C3—62no—
1066C22×C3—62no—
1067C22×C3—62no—
1068C22×C3#100914yes—
1069C22×C3C24×D312yes—
1070C2×D3—22no—
1071C2×D3—22no—
1072C2×D3—22no—
1073C2×D3—22no—
1074C2×D3—22no—
1075C2×D3—22no—
1076C2×D3—34no—
1077C2×D3—62no—
1078C2×D3—62no—
1079C2×D3—62no—
1080C2×D3—62no—
1081C2×D3—62no—
1082C2×D3—62no—
1083C2×D3—62no—
1084C2×D3—62no—
1085C2×D3—62no—
1086C2×D3—62no—
1087C2×D3—62no—
1088C2×D3—62no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—62no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—121no—
1097C2×D3—121no—
1098C2×D3—121no—
1099C2×D3—121no—
1100C2×D3—122no—
1101C2×D3—122no—
1102C2×D3—122no—
1103C2×D3—122no—
1104C2×D3—122no—
1105C2×D3—122no—
1106C2×D3—128no—
1107C2×D3—128no—
1108C2×D3—244no—
1109C2×D3—244no—
1110C2×D3—244no—
1111C2×D3—244no—
1112C2×D3—244no—
1113C2×D3—248no—
1114C3×C4—22no—
1115C3×C4—22no—
1116C3×C4—22no—
1117C3×C4—22no—
1118C3×C4—22no—
1119C3×C4—22no—
1120C3×C4—22no—
1121C3×C4—22no—
1122C3×C4—42no—
1123C3×C4—42no—
1124C3×C4—62no—
1125C3×C4—62no—
1126C3×C4—62no—
1127C3×C4—62no—
1128C3×C4—62no—
1129C3×C4—62no—
1130Dic3—22no—
1131Dic3—22no—
1132Dic3—22no—
1133Dic3—22no—
1134Dic3—22no—
1135Dic3—22no—
1136Dic3—62no—
1137Dic3—62no—
1138Dic3—121no—
1139Dic3—121no—
1140C32#353411yescharacteristic, complemented, Sylow
1141C23—32no—
1142C23—32no—
1143C23—91no—
1144C23—92no—
1145C23—91no—
1146C23—92no—
1147C23—182no—
1148C23—182no—
1149C23—182no—
1150C23—184no—
1151C23—361no—
1152C23—362no—
1153C23—362no—
1154C23—362no—
1155C23—361no—
1156C23—362no—
1157C23—362no—
1158C23—361no—
1159C23C22×D3211yescharacteristic
1160Q8—122no—
1161Q8—361no—
1162D4—64no—
1163D4—64no—
1164D4—122no—
1165D4—184no—
1166D4—184no—
1167D4—184no—
1168D4—361no—
1169D4—362no—
1170D4—361no—
1171D4—362no—
1172D4—362no—
1173D4—362no—
1174D4—362no—
1175D4—362no—
1176D4—362no—
1177D4—362no—
1178D4—362no—
1179D4—362no—
1180D4—362no—
1181D4—361no—
1182C2×C4—22no—
1183C2×C4—32no—
1184C2×C4—32no—
1185C2×C4—32no—
1186C2×C4—32no—
1187C2×C4—32no—
1188C2×C4—32no—
1189C2×C4—42no—
1190C2×C4—91no—
1191C2×C4—91no—
1192C2×C4—122no—
1193C2×C4—122no—
1194C2×C4—182no—
1195C2×C4—182no—
1196C2×C4—361no—
1197C2×C4—361no—
1198C2×C4—361no—
1199C2×C4—361no—
1200C2×C4—361no—
1201C2×C4—362no—
1202C2×C4—362no—
1203C2×C4—361no—
1204C2×C4—362no—
1205C2×C4—362no—
1206C2×C4C22×D3212yes—
1207C2×C4C22×D3212yes—
1208C2×C4C22×D3211yescharacteristic
1209C2×C4C22×D3211yescharacteristic
1210C2×C3—24no—
1211C2×C3—24no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—122no—
1216C2×C3—122no—
1217C2×C3C2×#100912yes—
1218C2×C3D3×H(5,𝔽2)12yes—
1219C2×C3#596812yes—
1220D3—42no—
1221D3—42no—
1222D3—64no—
1223D3—122no—
1224D3—122no—
1225D3—122no—
1226D3—122no—
1227D3—122no—
1228D3—122no—
1229D3—122no—
1230D3—242no—
1231D3—242no—
1232C22—21no—
1233C22—21no—
1234C22—62no—
1235C22—62no—
1236C22—62no—
1237C22—62no—
1238C22—62no—
1239C22—62no—
1240C22—92no—
1241C22—181no—
1242C22—181no—
1243C22—181no—
1244C22—182no—
1245C22—182no—
1246C22—182no—
1247C22—182no—
1248C22—181no—
1249C22—182no—
1250C22—181no—
1251C22—182no—
1252C22—364no—
1253C22—724no—
1254C22—722no—
1255C22—724no—
1256C22#6430812yes—
1257C22C23×D3211yescharacteristic
1258C4—21no—
1259C4—21no—
1260C4—22no—
1261C4—22no—
1262C4—62no—
1263C4—62no—
1264C4—62no—
1265C4—62no—
1266C4—62no—
1267C4—62no—
1268C4—181no—
1269C4—181no—
1270C3—21no—
1271C3#8645812yescomplemented
1272C2—22no—
1273C2—122no—
1274C2—122no—
1275C2—182no—
1276C2—361no—
1277C2—362no—
1278C2—362no—
1279C2C2×#6430811yescharacteristic
1280C2#1059667511yescharacteristic
1281C2#1059668911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64104C2semidirect
2. C3×#5515C2semidirect
3. #10595080C2semidirect
4. #10595079C2semidirect
5. #10595075C2semidirect
6. #10595074C2semidirect
7. #10595035C2semidirect
8. #10595018C2semidirect
9. #10594920C2semidirect
10. #10594663C2semidirect
11. #10594658C2semidirect
12. #10594652C2semidirect
13. #10594620C2semidirect
14. #10594610C2semidirect
15. #10594593C2semidirect
16. #10594519C2semidirect
17. #10594483C2semidirect
18. #10594468C2semidirect
19. #10594467C2semidirect
21. C22×C4⋊(C3⋊D3)C22semidirect
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C2×#3811C22semidirect
26. C2×#3805C22semidirect
27. C2×D3×D12C22semidirect
28. C2×#3799C22semidirect
29. C2×C32×C4⋊C4C22semidirect
30. C2×#3752C22semidirect
32. #64104C22semidirect
33. #64104C22semidirect
34. #64104C22semidirect
35. #64104C22semidirect
36. #64104C22semidirect
38. C3×#929C22semidirect
39. C3×#929C22semidirect
40. C3×C4×#67C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#924C22semidirect
43. C3×#898C22semidirect
44. C3×#898C22semidirect
45. C3×#896C22semidirect
46. C3×#896C22semidirect
47. C3×#894C22semidirect
48. C3×#894C22semidirect
49. C3×#889C22semidirect
50. C3×#889C22semidirect
52. #63981C22semidirect
53. #63981C22semidirect
54. #63974C22semidirect
55. #63974C22semidirect
56. #63962C22semidirect
57. #63957C22semidirect
58. #63923C22semidirect
59. #63923C22semidirect
60. #63923C22semidirect
61. #63923C22semidirect
62. #63922C22semidirect
63. #63921C22semidirect
64. #63921C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63912C22semidirect
67. #63912C22semidirect
68. #63911C22semidirect
69. #63910C22semidirect
70. #63910C22semidirect
71. #63910C22semidirect
72. #63910C22semidirect
73. #63910C22semidirect
74. #63910C22semidirect
75. #63910C22semidirect
76. #63910C22semidirect
77. #63909C22semidirect
78. #63909C22semidirect
79. #63907C22semidirect
80. #63906C22semidirect
81. #63904C22semidirect
82. #63897C22semidirect
83. #63897C22semidirect
84. #63897C22semidirect
85. #63897C22semidirect
86. #63895C22semidirect
87. #63894C22semidirect
88. #63894C22semidirect
89. #63890C22semidirect
90. #63888C22semidirect
91. #63886C22semidirect
92. #63883C22semidirect
93. #63883C22semidirect
94. #63881C22semidirect
95. #63881C22semidirect
96. #63880C22semidirect
97. #63868C22semidirect
98. #63865C22semidirect
99. #63865C22semidirect
100. #63864C22semidirect
101. #63854C22semidirect
102. #63853C22semidirect
103. #63853C22semidirect
104. #63852C22semidirect
105. #63850C22semidirect
106. #63848C22semidirect
107. #63836C22semidirect
137. #5515D3semidirect
266. C2×C3×C4⋊C4C2×D3semidirect
282. #929C2×D3semidirect
283. #929C2×D3semidirect
285. C4×#67C2×D3semidirect
286. C4×#67C2×D3semidirect
291. #924C2×D3semidirect
295. #898C2×D3semidirect
296. #898C2×D3semidirect
302. #896C2×D3semidirect
303. #896C2×D3semidirect
342. #894C2×D3semidirect
343. #894C2×D3semidirect
352. #889C2×D3semidirect
353. #889C2×D3semidirect
801. C2×C4⋊C4D32semidirect
1140. C32#3534semidirect
1271. C3#86458semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#641042
C3×#55152
#105950802
#105950792
#105950752
#105950742
#105950352
#105950182
#105949202
#105946632
#105946582
#105946522
#105946202
#105946102
#105945932
#105945192
#105944832
#105944682
#105944672
#864583